Related papers: Visualizing Topological Importance: A Class-Driven…

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or…

In this paper, we propose a data-free method of extracting Impressions of each class from the classifier's memory. The Deep Learning regime empowers classifiers to extract distinct patterns (or features) of a given class from training data,…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…

Feature Selection techniques aim at finding a relevant subset of features that perform equally or better than the original set of features at explaining the behavior of data. Typically, features are extracted from feature ranking or subset…

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…

The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based…

In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…

We propose a general multi-class visual recognition model, termed the Classifier Graph, which aims to generalize and integrate ideas from many of today's successful hierarchical recognition approaches. Our graph-based model has the…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…